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Heavy Higgs Resonances for the Neutralino Relic Density in the Higgs Decoupling Limit of the CP--noninvariant Minimal Supersymmetric Standard Model

The lightest neutralino is a compelling candidate to account for cold dark matter in the universe in supersymmetric theories with $R$--parity. In the CP-invariant theory, the neutralino relic density can be found in accord with recent WMAP data if neutralino annihilation in the early universe occurs via the s-channel $A$ funnel. In contrast, in the CP-noninvariant theory two heavy neutral Higgs bosons can contribute to the Higgs funnel mechanism significantly due to a CP-violating {\it complex} mixing between two heavy states, in particular, when they are almost degenerate. With a simple analytic and numerical analysis, we demonstrate that the CP-violating Higgs mixing can modify the profile of the neutralino relic density {\it considerably} in the heavy Higgs funnel with the neutralino mass close to half of the heavy Higgs masses.